E. Győri

activity

20142024

most citedThe Maximum Number of Pentagons in a Planar Graph

7 citations · 19 across the 13 of their papers we have counts for

collaborators

16 papers

math.CO2024

Jones' conjecture for Halin graphs and a bit more

Pál Bärnkopf, Ervin Győri

We prove Jones' famous conjecture for Halin graphs and a somewhat more general class of graphs, too. A based planar graph is a planar one that has a face adjacent to every other fa…

math.CO2023

Extending edge colorings of distance-3 matchings in the Cartesian product of graphs

Pál Bärnkopf, Ervin Győri

We investigate the problem of extending partial edge colorings in Cartesian products of graphs, with a particular focus on cases where the precolored edges form a matching. Casselg…

math.CO2023★ 1 cited

A new construction for planar Turán number of cycle

Ervin Győri, Kitti Varga, Xiutao Zhu

The planar Turán number $ex_{P} (n, C_{k})$ is the largest number of edges in an $n$ -vertex planar graph with no cycle of length $k$ . Let $k \geq 11$ and $C, D$ be constan…

math.CO2022

The maximum number of cliques in graphs with bounded odd circumference

Zequn Lv, Ervin Győri, Zhen He +3

In this work, we give the sharp upper bound for the number of cliques in graphs with bounded odd circumferences. This generalized Turán-type result is an extension of the celebrate…

math.CO2022

Exact results for generalized extremal problems forbidding an even cycle

Ervin Győri, Zhen He, Zequn Lv +4

We determine the maximum number of copies of $K_{s, s}$ in a $C_{2 s + 2}$ -free $n$ -vertex graph for all integers $s \geq 2$ and sufficiently large $n$ . Moreover, for $s \in {2, 3}$ and…

math.CO2022★ 1 cited

Stability version of Dirac's theorem and its applications for generalized Turán problems

Xiutao Zhu, Ervin Győri, Zhen He +3

In 1952, Dirac proved that every $2$ -connected $n$ -vertex graph with the minimum degree $k + 1$ contains a cycle of length at least $min {n, 2 (k + 1)}$ . Here we obtain a stability ve…

math.CO2021★ 1 cited

Extremal problems of double stars

Ervin Győri, Runze Wang, Spencer Woolfson

In a generalized Turán problem, two graphs $H$ and $F$ are given and the question is the maximum number of copies of $H$ in an $F$ -free graph of order $n$ . In this paper, we study…

math.CO2020

Planar Turán Number of the $Θ_{6}$

Debarun Ghosh, Ervin Győri, Addisu Paulos +2

Let $F$ be a nonempty family of graphs. A graph $G$ is called $F$ -\textit{free} if it contains no graph from $F$ as a subgraph. For a positive integer…

math.CO2020★ 1 cited

The Minimum Number of $4$ -Cycles in a Maximal Planar Graph with Small Number of Vertices

Ervin Győri, Addisu Paulos, Oscar Zamora

Hakimi and Schmeichel determined a sharp lower bound for the number of cycles of length 4 in a maximal planar graph with $n$ vertices, $n \geq 5$ . It has been shown that the bound i…

math.CO2020

The maximum number of induced $C_{5}$ 's in a planar graph

Debarun Ghosh, Ervin Győri, Oliver Janzer +3

Finding the maximum number of induced cycles of length $k$ in a graph on $n$ vertices has been one of the most intriguing open problems of Extremal Graph Theory. Recently Balogh, H…

math.CO2019★ 2 cited

The Maximum Number of Paths of Length Three in a Planar Graph

Andrzej Grzesik, Ervin Győri, Addisu Paulos +3

Let $f (n, H)$ denote the maximum number of copies of $H$ possible in an $n$ -vertex planar graph. The function $f (n, H)$ has been determined when $H$ is a cycle of length $3$ or $4$ b…

math.CO2019★ 7 cited

The Maximum Number of Pentagons in a Planar Graph

Ervin Győri, Addisu Paulos, Nika Salia +2

In 1979, Hakimi and Schmeichel considered the problem of maximizing the number of cycles of a given length in an $n$ -vertex planar graph. They precisely determined the maximum numb…

math.CO2017★ 5 cited

Turán number of an induced complete bipartite graph plus an odd cycle

Beka Ergemlidze, Ervin Győri, Abhishek Methuku

Let $k \geq 2$ be an integer. We show that if $s = 2$ and $t \geq 2$ , or $s = t = 3$ , then the maximum possible number of edges in a $C_{2 k + 1}$ -free graph containing no induced copy…

math.CO2017★ 1 cited

Mobile vs. point guards

Ervin Győri, Tamás Róbert Mezei

We study the problem of guarding orthogonal art galleries with horizontal mobile guards (alternatively, vertical) and point guards, using "rectangular vision". We prove a sharp bou…

math.CO2015

Toward Żak's conjecture on graph packing

Ervin Győri, Alexandr Kostochka, Andrew McConvey +1

Two graphs $G_{1} = (V_{1}, E_{1})$ and $G_{2} = (V_{2}, E_{2})$ , each of order $n$ , pack if there exists a bijection $f$ from $V_{1}$ onto $V_{2}$ such that $uv \in E_{1}$ implies…

math.CO2014

On $3$ -uniform hypergraphs without linear cycles

András Gyárfás, Ervin Győri, Miklós Simonovits

We explore properties of $3$ -uniform hypergraphs $H$ without linear cycles. Our main results are that these hypergraphs must contain a vertex of strong degree at most two and must…